Solve for $x$ and $y$ using elimination. ${-6x+3y = -33}$ ${-5x-5y = -50}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${-30x+15y = -165}$ $-15x-15y = -150$ Add the top and bottom equations together. $-45x = -315$ $\dfrac{-45x}{{-45}} = \dfrac{-315}{{-45}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-6x+3y = -33}\thinspace$ to find $y$ ${-6}{(7)}{ + 3y = -33}$ $-42+3y = -33$ $-42{+42} + 3y = -33{+42}$ $3y = 9$ $\dfrac{3y}{{3}} = \dfrac{9}{{3}}$ ${y = 3}$ You can also plug ${x = 7}$ into $\thinspace {-5x-5y = -50}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - 5y = -50}$ ${y = 3}$